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Uniform Strong Law of Large Numbers for Random Signed Measures

  • O. I. Klesov
  • I. MolchanovEmail author
Chapter
Part of the Understanding Complex Systems book series (UCS)

Abstract

We prove a strong law of large numbers for random signed measures on Euclidean space that holds uniformly over a family of arguments (sets) scaled by diagonal matrices. Applications to random measures generated by sums of random variables, marked point processes and stochastic integrals are also presented.

Notes

Acknowledgements

The authors are grateful to Andrii Ilienko for criticism and valuable comments that allow them to fill some gaps in the preliminary version of the manuscript.

This research was supported by the Swiss National Science Foundation Grant IZ7320_152292.

O.I. Klesov was supported by the grant 0118U003614 from Ministry of Education and Science of Ukraine (project N 2105 Φ).

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Authors and Affiliations

  1. 1.National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”Department of Mathematical Analysis and Probability TheoryKyivUkraine
  2. 2.University of BernInstitute of Mathematical Statistics and Actuarial ScienceBernSwitzerland

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